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Volumn 208, Issue 2, 2007, Pages 552-570

Asymptotic results for a multi-type contact birth-death process and related SIS epidemic

Author keywords

Asymptotic behaviour; Contact birth death process; Contact continuous space models; Convergence in probability; Deterministic SIS epidemic; Speed of spread

Indexed keywords

ASYMPTOTIC ANALYSIS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBABILITY;

EID: 34547120746     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.11.008     Document Type: Article
Times cited : (4)

References (27)
  • 2
    • 34547134009 scopus 로고    scopus 로고
    • V. Capasso, Mathematical Structures of Epidemic Systems, Lecture Notes in Biomathematics 97, Springer, Berlin, Heidelberg, 1993.
  • 3
    • 0016135893 scopus 로고
    • Geographic and temporal development of plagues
    • Nobel J. Geographic and temporal development of plagues. Nature 250 (1974) 726
    • (1974) Nature , vol.250 , pp. 726
    • Nobel, J.1
  • 4
    • 34547105120 scopus 로고    scopus 로고
    • D.G. Kendall, Mathematical models of the spread of infection, Mathematics and Computer Science in Biology and Medicine, H.M.S.O. london, (1965) 213.
  • 5
    • 0001047828 scopus 로고
    • Long term behaviour of a class of biological models
    • Weinberger H.F. Long term behaviour of a class of biological models. SIAM J. Math. Anal. 13 (1982) 353
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 353
    • Weinberger, H.F.1
  • 6
    • 0000327060 scopus 로고
    • A nonlinear integral operator arising from a model in population genetics, I. Monotone initial data
    • Lui R. A nonlinear integral operator arising from a model in population genetics, I. Monotone initial data. SIAM J. Math. Anal. 13 (1982) 913
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 913
    • Lui, R.1
  • 7
    • 0000327061 scopus 로고
    • A nonlinear integral operator arising from a model in population genetics, I. Initial data with compact support
    • Lui R. A nonlinear integral operator arising from a model in population genetics, I. Initial data with compact support. SIAM J. Math. Anal. 13 (1982) 938
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 938
    • Lui, R.1
  • 11
    • 34547133780 scopus 로고    scopus 로고
    • H.F. Weinberger, Asymptotic behaviour of a class of discrete time models in population genetics, Proc. Third Internat. Conf. Applied Nonlinear Analysis, Arlington TX: Academic, New York, London (1979) 407.
  • 12
  • 13
    • 38249039995 scopus 로고
    • Discrete-time growth-dispersal models
    • Kot M., and Schaffer W.M. Discrete-time growth-dispersal models. Math. Biosci. 80 1 (1986) 109
    • (1986) Math. Biosci. , vol.80 , Issue.1 , pp. 109
    • Kot, M.1    Schaffer, W.M.2
  • 14
    • 0038710532 scopus 로고    scopus 로고
    • Spreading diseases: integro-differential equations old and new
    • Medlock J., and Kot M. Spreading diseases: integro-differential equations old and new. Math. Biosci. 184 2 (2003) 201
    • (2003) Math. Biosci. , vol.184 , Issue.2 , pp. 201
    • Medlock, J.1    Kot, M.2
  • 16
    • 0001944424 scopus 로고
    • Run for your life. A note on the asymptotic speed of propagation of an epidemic
    • Diekmann O. Run for your life. A note on the asymptotic speed of propagation of an epidemic. J. Differential Equations 33 (1979) 58
    • (1979) J. Differential Equations , vol.33 , pp. 58
    • Diekmann, O.1
  • 17
    • 0018570848 scopus 로고
    • Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread
    • Thieme H.R. Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. J. Math. Biol. 8 (1979) 173
    • (1979) J. Math. Biol. , vol.8 , pp. 173
    • Thieme, H.R.1
  • 18
    • 0022592111 scopus 로고
    • The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic
    • Radcliffe J., and Rass L. The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic. J. Math. Biol. 23 (1986) 341
    • (1986) J. Math. Biol. , vol.23 , pp. 341
    • Radcliffe, J.1    Rass, L.2
  • 19
    • 33746591257 scopus 로고    scopus 로고
    • Spreading speeds and traveling waves for a multi-type SIS epidemic model
    • Weng P., and Zhao X.-Q. Spreading speeds and traveling waves for a multi-type SIS epidemic model. J. Differential Equations 229 (2006) 270
    • (2006) J. Differential Equations , vol.229 , pp. 270
    • Weng, P.1    Zhao, X.-Q.2
  • 20
    • 33751552431 scopus 로고    scopus 로고
    • Asymptotic speeds of spread and traveling waves for monotone semiflows with applications
    • Liang X., and Zhao X.-Q. Asymptotic speeds of spread and traveling waves for monotone semiflows with applications. Comm. Pure Appl. Maths. 60 (2007) 1
    • (2007) Comm. Pure Appl. Maths. , vol.60 , pp. 1
    • Liang, X.1    Zhao, X.-Q.2
  • 21
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 4 (2000) 599
    • (2000) SIAM Rev. , vol.42 , Issue.4 , pp. 599
    • Hethcote, H.W.1
  • 23
    • 21344435220 scopus 로고
    • The growth and spread of the general branching random walk
    • Biggins J.D. The growth and spread of the general branching random walk. Ann. Appl. Prob. 5 (1995) 1008
    • (1995) Ann. Appl. Prob. , vol.5 , pp. 1008
    • Biggins, J.D.1
  • 24
    • 84972503934 scopus 로고
    • Limits of spatial branching processes
    • Wakolbinger A. Limits of spatial branching processes. Bernoulli 1 1/2 (1995) 171
    • (1995) Bernoulli , vol.1 , Issue.1-2 , pp. 171
    • Wakolbinger, A.1
  • 25
    • 84968494996 scopus 로고
    • Crabgrass, measles and gypsy moths: an introduction to modern probability
    • Durrett R. Crabgrass, measles and gypsy moths: an introduction to modern probability. Bull. Amer. Math. Soc. 18 (1988) 117
    • (1988) Bull. Amer. Math. Soc. , vol.18 , pp. 117
    • Durrett, R.1
  • 26
    • 0036725475 scopus 로고    scopus 로고
    • Analysis of linear determinacy for spread in cooperative models
    • Weinberger R.F., Lewis M.A., and Li B. Analysis of linear determinacy for spread in cooperative models. J. Math. Biol. 45 (2002) 183
    • (2002) J. Math. Biol. , vol.45 , pp. 183
    • Weinberger, R.F.1    Lewis, M.A.2    Li, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.